Cesàro平均的带权强求和

Strong Summabieity with Weights for Cesàro Means

设 f(x) ∈LP(Ωn) ,1≤P ≤ 2 ,δ >(n- 1) (1P - 12 ) ,σδN(f) (x)表示 f(x)在n维球面Ωn 上的Ces劋ｒｏ平均っ髁恕 imN→∞1N+ 1ΣNk=0 ｜σδk(f) (x) - f(x) ｜2 ak =0 a .e .x∈Ωn其中权系数ak >0 ,满足 1≤ 1N+ 1ΣNk =0 ak ≤A (A是一个绝对常数 )。

Let f∈L P(Ω n),1≤P≤2,δ>(n-1)(1P-12), and σ δ N(f)(x) denotes the Cesàro means of f on n sphere Ω n. It is prorecl that lim N→∞1N+1∑Nk=0|σ δ k(f)(x)-f(x)| 2a k=0 a.e. x∈Ω n where a k≥0 and satisfy 1≤1N+1∑Nk=0a k≤A (A is an absolute constant ).